Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statement:
All players are cricketers.
Some players are robots.
Conclusions:
I. Some cricketers are players.
II. Some cricketers are robots.
Logical Reasoning Analysis: Statements and Conclusions
This problem requires us to analyze two given statements and determine if the two conclusions logically follow from them. We must assume the statements are true, even if they seem unusual.
Statements:
- Statement 1: All players are cricketers.
- Statement 2: Some players are robots.
Conclusions:
- Conclusion I: Some cricketers are players.
- Conclusion II: Some cricketers are robots.
Let's represent the sets involved:
- Let P be the set of all players.
- Let C be the set of all cricketers.
- Let R be the set of all robots.
We can express the statements using logical notation:
- Statement 1 translates to: $ \forall x (\text{Player}(x) \implies \text{Cricketer}(x)) $. This means if someone is a player, they are definitely a cricketer. The set P is a subset of C ($ P \subseteq C $).
- Statement 2 translates to: $ \exists x (\text{Player}(x) \land \text{Robot}(x)) $. This means there exists at least one person who is both a player and a robot. There is an overlap between sets P and R.
Evaluating Conclusion I
Conclusion I: Some cricketers are players.
From Statement 1, we know that "All players are cricketers." This means every individual in the set P is also in the set C.
If we take any individual who is a player, they must also be a cricketer. Therefore, it is true that at least some cricketers are players (specifically, those who are players).
In set notation, since $ P \subseteq C $, it implies that the intersection of C and P is non-empty if P is non-empty. The statement "All players..." implies the existence of players. Hence, $ C \cap P \neq \emptyset $. This confirms Conclusion I logically follows.
Symbolically, from $ \forall x (\text{Player}(x) \implies \text{Cricketer}(x)) $, we can infer $ \exists x (\text{Player}(x) \land \text{Cricketer}(x)) $ (assuming players exist).
Evaluating Conclusion II
Conclusion II: Some cricketers are robots.
From Statement 2, we know that "Some players are robots." This means there exists at least one individual who is both a player and a robot.
Let's consider such an individual, call them 'Alex'. Alex is a player and Alex is a robot.
From Statement 1, we know that "All players are cricketers." Since Alex is a player, Alex must also be a cricketer.
So, we have established that Alex is a cricketer and Alex is a robot.
Therefore, it logically follows that "Some cricketers are robots."
Symbolically, we have $ \exists x (\text{Player}(x) \land \text{Robot}(x)) $. From Statement 1, $ \forall y (\text{Player}(y) \implies \text{Cricketer}(y)) $. If we take the individual 'x' from Statement 2, we know Player(x) is true. From Statement 1, since Player(x) is true, Cricketer(x) must also be true. Since Robot(x) is also true (from Statement 2), we have $ \text{Cricketer}(x) \land \text{Robot}(x) $. This confirms Conclusion II logically follows.
Final Decision
Both Conclusion I and Conclusion II logically follow from the given statements.
Therefore, the correct option is the one stating that both conclusions follow.
Similar Questions
Two statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
No book is a novel.
All novels are diaries.
Conclusions:
I. All diaries can never be books.
II. Some books are diaries.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All rhombuses are tangents.
All chords are tangents.
Conclusions:
I. Some rhombuses being chords is a possibility.
II. Some tangents are rhombuses.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements :
Some C are P.
No C is a T.
All P are S.
Conclusions :
I. All S being C is a possibility.
II. At least some T are not C.
III. Some P are not T's.
Three statements are followed by three conclusions numbered I, II, III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follows from the given statements.
Statements :
No Mango is a banana.
No banana is a guava.
Some guavas are oranges.
Conclusions :
(I) Some mangoes are oranges.
(II) Some guavas are mangoes.
(III) No orange is a banana.
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All tigers are fishes.
No elephant is a tiger.
Some deer are tigers.
Conclusions:
I. Some fishes are deer.
II. No elephant is a deer.
III. No deer is a fish.
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statement :
All Bananas are Grapes.
All Papayas are Pineapple.
Some Pineapples are Banana.
Conclusions:
(I) Some Papayas are Grapes.
(II) Some Grapes are Pineapples.
(III) Some Bananas are Papayas.
Two statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All cups are saucers.
No saucer is a plate.
Conclusions:
I. Some cups are plates.
II. No cup is a plate.
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some cubs are trucks.
All trucks are lanterns.
No lanterns are bricks.
Conclusions:
I. Some cubs are lanterns.
II. Some trucks are not bricks.
III. All cubs are trucks.
Two statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
No locks are keys.
Some keys are passwords.
Conclusions:
I. Some passwords are locks.
II. All passwords are locks.
Two statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some defects are problems.
Some problems are solutions.
Conclusions:
I. Some defects being solutions is a possibility.
II. No solution is a defect.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
